What is $(a^3+b^3)\div(a^2-ab+b^2)$ when $a=5$ and $b=4$?
Explanation: Let's substitute the given values into the expression. We get  \begin{align*}
(a^3+b^3)\div(a^2-ab+b^2)&=(5^3+4^3)\div(5^2-5\cdot4+4^2)\\
&=(125+64)\div(25-20+16)\\
&=189\div21\\
&=\boxed{9}.
\end{align*}